Suppose that (P\(_{i,d_0}\) ) holds for some \(1\le d_0< d\) ; note that (P\(_{i,1}\) ) is vacuous. In [1]}, it was calculated that
\(\frac{\partial z}{\partial t}=\exp \left(-\int _0^{s} \frac{\partial f_i}{\partial z} \big (R_{i,j}(\sigma , t)\big ) \,\mathrm {d}\sigma \right)\) 
